The objective of this research is the development of the theory of lattice transformations as used in image processing and the application of the theory to two specific areas: mapping lattice transforms to special architectures, and the development of morphological neural networks. Lattice transforms, which include the transforms of mathematical morphology, are described by minimax algebra, a mathematical structure that mimics many properties of linear algebra. A high-level image processing language called image algebra provides the link between minimax algebra and lattice transforms. This research proposes to extend the mathematical foundations of minimax algebra in areas which will advance solutions to image processing problems. Specifically, decomposition techniques will be developed that will increase the tools available for mapping lattice transforms to parallel and sequential architectures with reduced computation. The initial investigation will seek to mimic linear techniques using minimax algebra. Also, a theory of novel neural computation involving morphological-type operations will be broadened by developing training rules and identifying-applications for this new type of neural network. The significance of the proposed research to the state- of-the-art is that it aims to increase the theoretical tools available for performing lattice-related image processing analysis in two important areas, transform decomposition and neural computing.
